Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set - Page 393: 22

$t-5$

When subtracting two fractions with common denominators, we subtract the numerators and copy the denominator. Therefore, the given expression, $ \dfrac{t^2}{t-3}-\dfrac{8t-15}{t-3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{t^2-(8t-15)}{t-3} \\\\= \dfrac{t^2-8t+15}{t-3} \\\\= \dfrac{(t-5)(t-3)}{t-3} \\\\= \dfrac{(t-5)(\cancel{t-3})}{\cancel{t-3}} \\\\= t-5 .\end{array}